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version 1.7, 2010/12/21 13:53:47 version 1.8, 2011/11/21 20:43:13
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   *> \brief \b ZHSEIN
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZHSEIN + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhsein.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhsein.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhsein.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
   *                          LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
   *                          IFAILR, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          EIGSRC, INITV, SIDE
   *       INTEGER            INFO, LDH, LDVL, LDVR, M, MM, N
   *       ..
   *       .. Array Arguments ..
   *       LOGICAL            SELECT( * )
   *       INTEGER            IFAILL( * ), IFAILR( * )
   *       DOUBLE PRECISION   RWORK( * )
   *       COMPLEX*16         H( LDH, * ), VL( LDVL, * ), VR( LDVR, * ),
   *      $                   W( * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHSEIN uses inverse iteration to find specified right and/or left
   *> eigenvectors of a complex upper Hessenberg matrix H.
   *>
   *> The right eigenvector x and the left eigenvector y of the matrix H
   *> corresponding to an eigenvalue w are defined by:
   *>
   *>              H * x = w * x,     y**h * H = w * y**h
   *>
   *> where y**h denotes the conjugate transpose of the vector y.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] SIDE
   *> \verbatim
   *>          SIDE is CHARACTER*1
   *>          = 'R': compute right eigenvectors only;
   *>          = 'L': compute left eigenvectors only;
   *>          = 'B': compute both right and left eigenvectors.
   *> \endverbatim
   *>
   *> \param[in] EIGSRC
   *> \verbatim
   *>          EIGSRC is CHARACTER*1
   *>          Specifies the source of eigenvalues supplied in W:
   *>          = 'Q': the eigenvalues were found using ZHSEQR; thus, if
   *>                 H has zero subdiagonal elements, and so is
   *>                 block-triangular, then the j-th eigenvalue can be
   *>                 assumed to be an eigenvalue of the block containing
   *>                 the j-th row/column.  This property allows ZHSEIN to
   *>                 perform inverse iteration on just one diagonal block.
   *>          = 'N': no assumptions are made on the correspondence
   *>                 between eigenvalues and diagonal blocks.  In this
   *>                 case, ZHSEIN must always perform inverse iteration
   *>                 using the whole matrix H.
   *> \endverbatim
   *>
   *> \param[in] INITV
   *> \verbatim
   *>          INITV is CHARACTER*1
   *>          = 'N': no initial vectors are supplied;
   *>          = 'U': user-supplied initial vectors are stored in the arrays
   *>                 VL and/or VR.
   *> \endverbatim
   *>
   *> \param[in] SELECT
   *> \verbatim
   *>          SELECT is LOGICAL array, dimension (N)
   *>          Specifies the eigenvectors to be computed. To select the
   *>          eigenvector corresponding to the eigenvalue W(j),
   *>          SELECT(j) must be set to .TRUE..
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix H.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] H
   *> \verbatim
   *>          H is COMPLEX*16 array, dimension (LDH,N)
   *>          The upper Hessenberg matrix H.
   *> \endverbatim
   *>
   *> \param[in] LDH
   *> \verbatim
   *>          LDH is INTEGER
   *>          The leading dimension of the array H.  LDH >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in,out] W
   *> \verbatim
   *>          W is COMPLEX*16 array, dimension (N)
   *>          On entry, the eigenvalues of H.
   *>          On exit, the real parts of W may have been altered since
   *>          close eigenvalues are perturbed slightly in searching for
   *>          independent eigenvectors.
   *> \endverbatim
   *>
   *> \param[in,out] VL
   *> \verbatim
   *>          VL is COMPLEX*16 array, dimension (LDVL,MM)
   *>          On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must
   *>          contain starting vectors for the inverse iteration for the
   *>          left eigenvectors; the starting vector for each eigenvector
   *>          must be in the same column in which the eigenvector will be
   *>          stored.
   *>          On exit, if SIDE = 'L' or 'B', the left eigenvectors
   *>          specified by SELECT will be stored consecutively in the
   *>          columns of VL, in the same order as their eigenvalues.
   *>          If SIDE = 'R', VL is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDVL
   *> \verbatim
   *>          LDVL is INTEGER
   *>          The leading dimension of the array VL.
   *>          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
   *> \endverbatim
   *>
   *> \param[in,out] VR
   *> \verbatim
   *>          VR is COMPLEX*16 array, dimension (LDVR,MM)
   *>          On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must
   *>          contain starting vectors for the inverse iteration for the
   *>          right eigenvectors; the starting vector for each eigenvector
   *>          must be in the same column in which the eigenvector will be
   *>          stored.
   *>          On exit, if SIDE = 'R' or 'B', the right eigenvectors
   *>          specified by SELECT will be stored consecutively in the
   *>          columns of VR, in the same order as their eigenvalues.
   *>          If SIDE = 'L', VR is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDVR
   *> \verbatim
   *>          LDVR is INTEGER
   *>          The leading dimension of the array VR.
   *>          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
   *> \endverbatim
   *>
   *> \param[in] MM
   *> \verbatim
   *>          MM is INTEGER
   *>          The number of columns in the arrays VL and/or VR. MM >= M.
   *> \endverbatim
   *>
   *> \param[out] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of columns in the arrays VL and/or VR required to
   *>          store the eigenvectors (= the number of .TRUE. elements in
   *>          SELECT).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is COMPLEX*16 array, dimension (N*N)
   *> \endverbatim
   *>
   *> \param[out] RWORK
   *> \verbatim
   *>          RWORK is DOUBLE PRECISION array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] IFAILL
   *> \verbatim
   *>          IFAILL is INTEGER array, dimension (MM)
   *>          If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left
   *>          eigenvector in the i-th column of VL (corresponding to the
   *>          eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the
   *>          eigenvector converged satisfactorily.
   *>          If SIDE = 'R', IFAILL is not referenced.
   *> \endverbatim
   *>
   *> \param[out] IFAILR
   *> \verbatim
   *>          IFAILR is INTEGER array, dimension (MM)
   *>          If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right
   *>          eigenvector in the i-th column of VR (corresponding to the
   *>          eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the
   *>          eigenvector converged satisfactorily.
   *>          If SIDE = 'L', IFAILR is not referenced.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  if INFO = i, i is the number of eigenvectors which
   *>                failed to converge; see IFAILL and IFAILR for further
   *>                details.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERcomputational
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Each eigenvector is normalized so that the element of largest
   *>  magnitude has magnitude 1; here the magnitude of a complex number
   *>  (x,y) is taken to be |x|+|y|.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,        SUBROUTINE ZHSEIN( SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL,
      $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,       $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL,
      $                   IFAILR, INFO )       $                   IFAILR, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          EIGSRC, INITV, SIDE        CHARACTER          EIGSRC, INITV, SIDE
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      $                   W( * ), WORK( * )       $                   W( * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHSEIN uses inverse iteration to find specified right and/or left  
 *  eigenvectors of a complex upper Hessenberg matrix H.  
 *  
 *  The right eigenvector x and the left eigenvector y of the matrix H  
 *  corresponding to an eigenvalue w are defined by:  
 *  
 *               H * x = w * x,     y**h * H = w * y**h  
 *  
 *  where y**h denotes the conjugate transpose of the vector y.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  SIDE    (input) CHARACTER*1  
 *          = 'R': compute right eigenvectors only;  
 *          = 'L': compute left eigenvectors only;  
 *          = 'B': compute both right and left eigenvectors.  
 *  
 *  EIGSRC  (input) CHARACTER*1  
 *          Specifies the source of eigenvalues supplied in W:  
 *          = 'Q': the eigenvalues were found using ZHSEQR; thus, if  
 *                 H has zero subdiagonal elements, and so is  
 *                 block-triangular, then the j-th eigenvalue can be  
 *                 assumed to be an eigenvalue of the block containing  
 *                 the j-th row/column.  This property allows ZHSEIN to  
 *                 perform inverse iteration on just one diagonal block.  
 *          = 'N': no assumptions are made on the correspondence  
 *                 between eigenvalues and diagonal blocks.  In this  
 *                 case, ZHSEIN must always perform inverse iteration  
 *                 using the whole matrix H.  
 *  
 *  INITV   (input) CHARACTER*1  
 *          = 'N': no initial vectors are supplied;  
 *          = 'U': user-supplied initial vectors are stored in the arrays  
 *                 VL and/or VR.  
 *  
 *  SELECT  (input) LOGICAL array, dimension (N)  
 *          Specifies the eigenvectors to be computed. To select the  
 *          eigenvector corresponding to the eigenvalue W(j),  
 *          SELECT(j) must be set to .TRUE..  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix H.  N >= 0.  
 *  
 *  H       (input) COMPLEX*16 array, dimension (LDH,N)  
 *          The upper Hessenberg matrix H.  
 *  
 *  LDH     (input) INTEGER  
 *          The leading dimension of the array H.  LDH >= max(1,N).  
 *  
 *  W       (input/output) COMPLEX*16 array, dimension (N)  
 *          On entry, the eigenvalues of H.  
 *          On exit, the real parts of W may have been altered since  
 *          close eigenvalues are perturbed slightly in searching for  
 *          independent eigenvectors.  
 *  
 *  VL      (input/output) COMPLEX*16 array, dimension (LDVL,MM)  
 *          On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must  
 *          contain starting vectors for the inverse iteration for the  
 *          left eigenvectors; the starting vector for each eigenvector  
 *          must be in the same column in which the eigenvector will be  
 *          stored.  
 *          On exit, if SIDE = 'L' or 'B', the left eigenvectors  
 *          specified by SELECT will be stored consecutively in the  
 *          columns of VL, in the same order as their eigenvalues.  
 *          If SIDE = 'R', VL is not referenced.  
 *  
 *  LDVL    (input) INTEGER  
 *          The leading dimension of the array VL.  
 *          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.  
 *  
 *  VR      (input/output) COMPLEX*16 array, dimension (LDVR,MM)  
 *          On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must  
 *          contain starting vectors for the inverse iteration for the  
 *          right eigenvectors; the starting vector for each eigenvector  
 *          must be in the same column in which the eigenvector will be  
 *          stored.  
 *          On exit, if SIDE = 'R' or 'B', the right eigenvectors  
 *          specified by SELECT will be stored consecutively in the  
 *          columns of VR, in the same order as their eigenvalues.  
 *          If SIDE = 'L', VR is not referenced.  
 *  
 *  LDVR    (input) INTEGER  
 *          The leading dimension of the array VR.  
 *          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.  
 *  
 *  MM      (input) INTEGER  
 *          The number of columns in the arrays VL and/or VR. MM >= M.  
 *  
 *  M       (output) INTEGER  
 *          The number of columns in the arrays VL and/or VR required to  
 *          store the eigenvectors (= the number of .TRUE. elements in  
 *          SELECT).  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (N*N)  
 *  
 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)  
 *  
 *  IFAILL  (output) INTEGER array, dimension (MM)  
 *          If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left  
 *          eigenvector in the i-th column of VL (corresponding to the  
 *          eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the  
 *          eigenvector converged satisfactorily.  
 *          If SIDE = 'R', IFAILL is not referenced.  
 *  
 *  IFAILR  (output) INTEGER array, dimension (MM)  
 *          If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right  
 *          eigenvector in the i-th column of VR (corresponding to the  
 *          eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the  
 *          eigenvector converged satisfactorily.  
 *          If SIDE = 'L', IFAILR is not referenced.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  if INFO = i, i is the number of eigenvectors which  
 *                failed to converge; see IFAILL and IFAILR for further  
 *                details.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Each eigenvector is normalized so that the element of largest  
 *  magnitude has magnitude 1; here the magnitude of a complex number  
 *  (x,y) is taken to be |x|+|y|.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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